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        <a href="numdifftools-module.html">Package&nbsp;numdifftools</a> ::
        Module&nbsp;nd_algopy
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<h1 class="epydoc">Source Code for <a href="numdifftools.nd_algopy-module.html">Module numdifftools.nd_algopy</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">  1</tt>  <tt class="py-line"><tt class="py-docstring">'''</tt> </tt>
<a name="L2"></a><tt class="py-lineno">  2</tt>  <tt class="py-line"><tt class="py-docstring">Easy to use interface to derivatives in algopy</tt> </tt>
<a name="L3"></a><tt class="py-lineno">  3</tt>  <tt class="py-line"><tt class="py-docstring">'''</tt> </tt>
<a name="L4"></a><tt class="py-lineno">  4</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">__future__</tt> <tt class="py-keyword">import</tt> <tt class="py-name">division</tt> </tt>
<a name="L5"></a><tt class="py-lineno">  5</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt> <tt class="py-keyword">as</tt> <tt class="py-name">np</tt> </tt>
<a name="L6"></a><tt class="py-lineno">  6</tt>  <tt class="py-line"><tt class="py-keyword">try</tt><tt class="py-op">:</tt> </tt>
<a name="L7"></a><tt class="py-lineno">  7</tt>  <tt class="py-line">    <tt class="py-keyword">import</tt> <tt class="py-name">algopy</tt> </tt>
<a name="L8"></a><tt class="py-lineno">  8</tt>  <tt class="py-line"><tt class="py-keyword">except</tt> <tt class="py-name">ImportError</tt><tt class="py-op">:</tt> </tt>
<a name="L9"></a><tt class="py-lineno">  9</tt>  <tt class="py-line">    <tt class="py-name">algopy</tt> <tt class="py-op">=</tt> <tt class="py-name">None</tt> </tt>
<a name="L10"></a><tt class="py-lineno"> 10</tt>  <tt class="py-line"> </tt>
<a name="_Common"></a><div id="_Common-def"><a name="L11"></a><tt class="py-lineno"> 11</tt> <a class="py-toggle" href="#" id="_Common-toggle" onclick="return toggle('_Common');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html">_Common</a><tt class="py-op">(</tt><tt class="py-base-class">object</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Common-expanded"><a name="_Common.__init__"></a><div id="_Common.__init__-def"><a name="L12"></a><tt class="py-lineno"> 12</tt> <a class="py-toggle" href="#" id="_Common.__init__-toggle" onclick="return toggle('_Common.__init__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#__init__">__init__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">fun</tt><tt class="py-op">,</tt> <tt class="py-param">method</tt><tt class="py-op">=</tt><tt class="py-string">'forward'</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common.__init__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common.__init__-expanded"><a name="L13"></a><tt class="py-lineno"> 13</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt> <tt class="py-op">=</tt> <tt class="py-name">fun</tt> </tt>
<a name="L14"></a><tt class="py-lineno"> 14</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt> <tt class="py-op">=</tt> <tt class="py-name">method</tt> </tt>
<a name="L15"></a><tt class="py-lineno"> 15</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-0" class="py-name" targets="Method numdifftools.nd_algopy._Common.initialize()=numdifftools.nd_algopy._Common-class.html#initialize"><a title="numdifftools.nd_algopy._Common.initialize" class="py-name" href="#" onclick="return doclink('link-0', 'initialize', 'link-0');">initialize</a></tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Common._initialize_reverse"></a><div id="_Common._initialize_reverse-def"><a name="L16"></a><tt class="py-lineno"> 16</tt> <a class="py-toggle" href="#" id="_Common._initialize_reverse-toggle" onclick="return toggle('_Common._initialize_reverse');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_initialize_reverse">_initialize_reverse</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._initialize_reverse-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._initialize_reverse-expanded"><a name="L17"></a><tt class="py-lineno"> 17</tt>  <tt class="py-line">        <tt class="py-comment">#x = np.asarray(x, dtype=float)</tt> </tt>
<a name="L18"></a><tt class="py-lineno"> 18</tt>  <tt class="py-line">        <tt class="py-comment">#self.x = x.copy()</tt> </tt>
<a name="L19"></a><tt class="py-lineno"> 19</tt>  <tt class="py-line">        <tt class="py-comment"># STEP 1: trace the function evaluation</tt> </tt>
<a name="L20"></a><tt class="py-lineno"> 20</tt>  <tt class="py-line">        <tt class="py-name">cg</tt> <tt class="py-op">=</tt> <tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">CGraph</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L21"></a><tt class="py-lineno"> 21</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">True</tt><tt class="py-op">:</tt> </tt>
<a name="L22"></a><tt class="py-lineno"> 22</tt>  <tt class="py-line">            <tt class="py-name">x</tt> <tt class="py-op">=</tt> <tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">Function</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
<a name="L23"></a><tt class="py-lineno"> 23</tt>  <tt class="py-line">            <tt class="py-comment">#x = [x]</tt> </tt>
<a name="L24"></a><tt class="py-lineno"> 24</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L25"></a><tt class="py-lineno"> 25</tt>  <tt class="py-line">            <tt class="py-name">x</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">array</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">Function</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">[</tt><tt class="py-name">i</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">i</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L26"></a><tt class="py-lineno"> 26</tt>  <tt class="py-line">         </tt>
<a name="L27"></a><tt class="py-lineno"> 27</tt>  <tt class="py-line">        <tt class="py-name">y</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
<a name="L28"></a><tt class="py-lineno"> 28</tt>  <tt class="py-line">        <tt class="py-name">cg</tt><tt class="py-op">.</tt><tt class="py-name">trace_off</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L29"></a><tt class="py-lineno"> 29</tt>  <tt class="py-line">        <tt class="py-name">cg</tt><tt class="py-op">.</tt><tt class="py-name">independentFunctionList</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">x</tt><tt class="py-op">]</tt> </tt>
<a name="L30"></a><tt class="py-lineno"> 30</tt>  <tt class="py-line">        <tt class="py-name">cg</tt><tt class="py-op">.</tt><tt class="py-name">dependentFunctionList</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">y</tt><tt class="py-op">]</tt> </tt>
<a name="L31"></a><tt class="py-lineno"> 31</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_cg</tt> <tt class="py-op">=</tt> <tt class="py-name">cg</tt> </tt>
</div><a name="_Common.initialize"></a><div id="_Common.initialize-def"><a name="L32"></a><tt class="py-lineno"> 32</tt> <a class="py-toggle" href="#" id="_Common.initialize-toggle" onclick="return toggle('_Common.initialize');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#initialize">initialize</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common.initialize-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common.initialize-expanded"><a name="L33"></a><tt class="py-lineno"> 33</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">method</tt><tt class="py-op">.</tt><tt class="py-name">startswith</tt><tt class="py-op">(</tt><tt class="py-string">'reverse'</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L34"></a><tt class="py-lineno"> 34</tt>  <tt class="py-line">            <tt class="py-comment"># reverse mode using a computational graph</tt> </tt>
<a name="L35"></a><tt class="py-lineno"> 35</tt>  <tt class="py-line">            <tt class="py-comment">#self._initialize_reverse(x)</tt> </tt>
<a name="L36"></a><tt class="py-lineno"> 36</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-1" class="py-name" targets="Method numdifftools.nd_scientific._Common._gradient()=numdifftools.nd_scientific._Common-class.html#_gradient"><a title="numdifftools.nd_scientific._Common._gradient" class="py-name" href="#" onclick="return doclink('link-1', '_gradient', 'link-1');">_gradient</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-2" class="py-name" targets="Method numdifftools.nd_algopy._Common._gradient_reverse()=numdifftools.nd_algopy._Common-class.html#_gradient_reverse"><a title="numdifftools.nd_algopy._Common._gradient_reverse" class="py-name" href="#" onclick="return doclink('link-2', '_gradient_reverse', 'link-2');">_gradient_reverse</a></tt> </tt>
<a name="L37"></a><tt class="py-lineno"> 37</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-3" class="py-name" targets="Method numdifftools.nd_scientific._Common._hessian()=numdifftools.nd_scientific._Common-class.html#_hessian"><a title="numdifftools.nd_scientific._Common._hessian" class="py-name" href="#" onclick="return doclink('link-3', '_hessian', 'link-3');">_hessian</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-4" class="py-name" targets="Method numdifftools.nd_algopy._Common._hessian_reverse()=numdifftools.nd_algopy._Common-class.html#_hessian_reverse"><a title="numdifftools.nd_algopy._Common._hessian_reverse" class="py-name" href="#" onclick="return doclink('link-4', '_hessian_reverse', 'link-4');">_hessian_reverse</a></tt> </tt>
<a name="L38"></a><tt class="py-lineno"> 38</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-5" class="py-name" targets="Method numdifftools.nd_scientific._Common._jacobian()=numdifftools.nd_scientific._Common-class.html#_jacobian"><a title="numdifftools.nd_scientific._Common._jacobian" class="py-name" href="#" onclick="return doclink('link-5', '_jacobian', 'link-5');">_jacobian</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-6" class="py-name" targets="Method numdifftools.nd_algopy._Common._jacobian_reverse()=numdifftools.nd_algopy._Common-class.html#_jacobian_reverse"><a title="numdifftools.nd_algopy._Common._jacobian_reverse" class="py-name" href="#" onclick="return doclink('link-6', '_jacobian_reverse', 'link-6');">_jacobian_reverse</a></tt>   </tt>
<a name="L39"></a><tt class="py-lineno"> 39</tt>  <tt class="py-line">        <tt class="py-keyword">else</tt><tt class="py-op">:</tt> <tt class="py-comment"># forward mode without building the computational graph</tt> </tt>
<a name="L40"></a><tt class="py-lineno"> 40</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-7" class="py-name"><a title="numdifftools.nd_scientific._Common._gradient" class="py-name" href="#" onclick="return doclink('link-7', '_gradient', 'link-1');">_gradient</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-8" class="py-name" targets="Method numdifftools.nd_algopy._Common._gradient_forward()=numdifftools.nd_algopy._Common-class.html#_gradient_forward"><a title="numdifftools.nd_algopy._Common._gradient_forward" class="py-name" href="#" onclick="return doclink('link-8', '_gradient_forward', 'link-8');">_gradient_forward</a></tt> </tt>
<a name="L41"></a><tt class="py-lineno"> 41</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-9" class="py-name"><a title="numdifftools.nd_scientific._Common._hessian" class="py-name" href="#" onclick="return doclink('link-9', '_hessian', 'link-3');">_hessian</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-10" class="py-name" targets="Method numdifftools.nd_algopy._Common._hessian_forward()=numdifftools.nd_algopy._Common-class.html#_hessian_forward"><a title="numdifftools.nd_algopy._Common._hessian_forward" class="py-name" href="#" onclick="return doclink('link-10', '_hessian_forward', 'link-10');">_hessian_forward</a></tt> </tt>
<a name="L42"></a><tt class="py-lineno"> 42</tt>  <tt class="py-line">            <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-11" class="py-name"><a title="numdifftools.nd_scientific._Common._jacobian" class="py-name" href="#" onclick="return doclink('link-11', '_jacobian', 'link-5');">_jacobian</a></tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-12" class="py-name"><a title="numdifftools.nd_algopy._Common._gradient_forward" class="py-name" href="#" onclick="return doclink('link-12', '_gradient_forward', 'link-8');">_gradient_forward</a></tt> </tt>
</div><a name="L43"></a><tt class="py-lineno"> 43</tt>  <tt class="py-line">            </tt>
<a name="_Common._derivative"></a><div id="_Common._derivative-def"><a name="L44"></a><tt class="py-lineno"> 44</tt> <a class="py-toggle" href="#" id="_Common._derivative-toggle" onclick="return toggle('_Common._derivative');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_derivative">_derivative</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._derivative-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._derivative-expanded"><a name="L45"></a><tt class="py-lineno"> 45</tt>  <tt class="py-line">        <tt class="py-name">xi</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">,</tt> <tt class="py-name">dtype</tt><tt class="py-op">=</tt><tt class="py-name">float</tt><tt class="py-op">)</tt> </tt>
<a name="L46"></a><tt class="py-lineno"> 46</tt>  <tt class="py-line">        <tt class="py-name">shape0</tt>  <tt class="py-op">=</tt> <tt class="py-name">xi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt> </tt>
<a name="L47"></a><tt class="py-lineno"> 47</tt>  <tt class="py-line">        <tt class="py-name">y</tt> <tt class="py-op">=</tt> <tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">array</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-13" class="py-name"><a title="numdifftools.nd_scientific._Common._gradient" class="py-name" href="#" onclick="return doclink('link-13', '_gradient', 'link-1');">_gradient</a></tt><tt class="py-op">(</tt><tt class="py-name">xj</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">xj</tt> <tt class="py-keyword">in</tt> <tt class="py-name">xi</tt><tt class="py-op">.</tt><tt class="py-name">ravel</tt><tt class="py-op">(</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt>  </tt>
<a name="L48"></a><tt class="py-lineno"> 48</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">y</tt><tt class="py-op">.</tt><tt class="py-name">reshape</tt><tt class="py-op">(</tt><tt class="py-name">shape0</tt><tt class="py-op">)</tt> </tt>
</div><a name="L49"></a><tt class="py-lineno"> 49</tt>  <tt class="py-line">    <tt class="py-comment">#def _jacobian(self, x):</tt> </tt>
<a name="L50"></a><tt class="py-lineno"> 50</tt>  <tt class="py-line">    <tt class="py-comment">#    return self._gradient(x) </tt> </tt>
<a name="_Common._jacobian_reverse"></a><div id="_Common._jacobian_reverse-def"><a name="L51"></a><tt class="py-lineno"> 51</tt> <a class="py-toggle" href="#" id="_Common._jacobian_reverse-toggle" onclick="return toggle('_Common._jacobian_reverse');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_jacobian_reverse">_jacobian_reverse</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._jacobian_reverse-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._jacobian_reverse-expanded"><a name="L52"></a><tt class="py-lineno"> 52</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-14" class="py-name" targets="Method numdifftools.nd_algopy._Common._initialize_reverse()=numdifftools.nd_algopy._Common-class.html#_initialize_reverse"><a title="numdifftools.nd_algopy._Common._initialize_reverse" class="py-name" href="#" onclick="return doclink('link-14', '_initialize_reverse', 'link-14');">_initialize_reverse</a></tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
<a name="L53"></a><tt class="py-lineno"> 53</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_cg</tt><tt class="py-op">.</tt><tt id="link-15" class="py-name" targets="Method numdifftools.core.Jacobian.jacobian()=numdifftools.core.Jacobian-class.html#jacobian,Method numdifftools.nd_algopy.Jacobian.jacobian()=numdifftools.nd_algopy.Jacobian-class.html#jacobian,Method numdifftools.nd_scientific.Jacobian.jacobian()=numdifftools.nd_scientific.Jacobian-class.html#jacobian"><a title="numdifftools.core.Jacobian.jacobian
numdifftools.nd_algopy.Jacobian.jacobian
numdifftools.nd_scientific.Jacobian.jacobian" class="py-name" href="#" onclick="return doclink('link-15', 'jacobian', 'link-15');">jacobian</a></tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Common._gradient_reverse"></a><div id="_Common._gradient_reverse-def"><a name="L54"></a><tt class="py-lineno"> 54</tt> <a class="py-toggle" href="#" id="_Common._gradient_reverse-toggle" onclick="return toggle('_Common._gradient_reverse');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_gradient_reverse">_gradient_reverse</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._gradient_reverse-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._gradient_reverse-expanded"><a name="L55"></a><tt class="py-lineno"> 55</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-16" class="py-name"><a title="numdifftools.nd_algopy._Common._initialize_reverse" class="py-name" href="#" onclick="return doclink('link-16', '_initialize_reverse', 'link-14');">_initialize_reverse</a></tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
<a name="L56"></a><tt class="py-lineno"> 56</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_cg</tt><tt class="py-op">.</tt><tt id="link-17" class="py-name" targets="Method numdifftools.core.Gradient.gradient()=numdifftools.core.Gradient-class.html#gradient,Method numdifftools.nd_algopy.Gradient.gradient()=numdifftools.nd_algopy.Gradient-class.html#gradient,Method numdifftools.nd_scientific.Gradient.gradient()=numdifftools.nd_scientific.Gradient-class.html#gradient"><a title="numdifftools.core.Gradient.gradient
numdifftools.nd_algopy.Gradient.gradient
numdifftools.nd_scientific.Gradient.gradient" class="py-name" href="#" onclick="return doclink('link-17', 'gradient', 'link-17');">gradient</a></tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Common._hessian_reverse"></a><div id="_Common._hessian_reverse-def"><a name="L57"></a><tt class="py-lineno"> 57</tt> <a class="py-toggle" href="#" id="_Common._hessian_reverse-toggle" onclick="return toggle('_Common._hessian_reverse');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_hessian_reverse">_hessian_reverse</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._hessian_reverse-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._hessian_reverse-expanded"><a name="L58"></a><tt class="py-lineno"> 58</tt>  <tt class="py-line">        <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-18" class="py-name"><a title="numdifftools.nd_algopy._Common._initialize_reverse" class="py-name" href="#" onclick="return doclink('link-18', '_initialize_reverse', 'link-14');">_initialize_reverse</a></tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
<a name="L59"></a><tt class="py-lineno"> 59</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">_cg</tt><tt class="py-op">.</tt><tt id="link-19" class="py-name" targets="Method numdifftools.core.Hessian.hessian()=numdifftools.core.Hessian-class.html#hessian,Method numdifftools.nd_algopy.Hessian.hessian()=numdifftools.nd_algopy.Hessian-class.html#hessian,Method numdifftools.nd_scientific.Hessian.hessian()=numdifftools.nd_scientific.Hessian-class.html#hessian"><a title="numdifftools.core.Hessian.hessian
numdifftools.nd_algopy.Hessian.hessian
numdifftools.nd_scientific.Hessian.hessian" class="py-name" href="#" onclick="return doclink('link-19', 'hessian', 'link-19');">hessian</a></tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
</div><a name="L60"></a><tt class="py-lineno"> 60</tt>  <tt class="py-line">        <tt class="py-comment">#return self._cg.hessian([x])</tt> </tt>
<a name="_Common._gradient_forward"></a><div id="_Common._gradient_forward-def"><a name="L61"></a><tt class="py-lineno"> 61</tt> <a class="py-toggle" href="#" id="_Common._gradient_forward-toggle" onclick="return toggle('_Common._gradient_forward');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_gradient_forward">_gradient_forward</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._gradient_forward-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._gradient_forward-expanded"><a name="L62"></a><tt class="py-lineno"> 62</tt>  <tt class="py-line">        <tt class="py-comment"># forward mode without building the computational graph</tt> </tt>
<a name="L63"></a><tt class="py-lineno"> 63</tt>  <tt class="py-line">        <tt class="py-name">tmp</tt> <tt class="py-op">=</tt> <tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">UTPM</tt><tt class="py-op">.</tt><tt class="py-name">init_jacobian</tt><tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">,</tt> <tt class="py-name">dtype</tt><tt class="py-op">=</tt><tt class="py-name">float</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L64"></a><tt class="py-lineno"> 64</tt>  <tt class="py-line">        <tt class="py-name">tmp2</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">tmp</tt><tt class="py-op">)</tt> </tt>
<a name="L65"></a><tt class="py-lineno"> 65</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">UTPM</tt><tt class="py-op">.</tt><tt class="py-name">extract_jacobian</tt><tt class="py-op">(</tt><tt class="py-name">tmp2</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Common._hessian_forward"></a><div id="_Common._hessian_forward-def"><a name="L66"></a><tt class="py-lineno"> 66</tt> <a class="py-toggle" href="#" id="_Common._hessian_forward-toggle" onclick="return toggle('_Common._hessian_forward');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy._Common-class.html#_hessian_forward">_hessian_forward</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Common._hessian_forward-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="_Common._hessian_forward-expanded"><a name="L67"></a><tt class="py-lineno"> 67</tt>  <tt class="py-line">        <tt class="py-name">tmp</tt> <tt class="py-op">=</tt> <tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">UTPM</tt><tt class="py-op">.</tt><tt class="py-name">init_hessian</tt><tt class="py-op">(</tt><tt class="py-name">np</tt><tt class="py-op">.</tt><tt class="py-name">asarray</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">,</tt> <tt class="py-name">dtype</tt><tt class="py-op">=</tt><tt class="py-name">float</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L68"></a><tt class="py-lineno"> 68</tt>  <tt class="py-line">        <tt class="py-name">tmp2</tt> <tt class="py-op">=</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt class="py-name">fun</tt><tt class="py-op">(</tt><tt class="py-name">tmp</tt><tt class="py-op">)</tt> </tt>
<a name="L69"></a><tt class="py-lineno"> 69</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">algopy</tt><tt class="py-op">.</tt><tt class="py-name">UTPM</tt><tt class="py-op">.</tt><tt class="py-name">extract_hessian</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">tmp2</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L70"></a><tt class="py-lineno"> 70</tt>  <tt class="py-line"> </tt>
<a name="Derivative"></a><div id="Derivative-def"><a name="L71"></a><tt class="py-lineno"> 71</tt> <a class="py-toggle" href="#" id="Derivative-toggle" onclick="return toggle('Derivative');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Derivative-class.html">Derivative</a><tt class="py-op">(</tt><tt class="py-base-class">_Common</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Derivative-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Derivative-expanded"><a name="L72"></a><tt class="py-lineno"> 72</tt>  <tt class="py-line">    <tt class="py-docstring">'''</tt> </tt>
<a name="L73"></a><tt class="py-lineno"> 73</tt>  <tt class="py-line"><tt class="py-docstring">    Estimate n'th derivative of fun at x0</tt> </tt>
<a name="L74"></a><tt class="py-lineno"> 74</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L75"></a><tt class="py-lineno"> 75</tt>  <tt class="py-line"><tt class="py-docstring">    Examples</tt> </tt>
<a name="L76"></a><tt class="py-lineno"> 76</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L77"></a><tt class="py-lineno"> 77</tt>  <tt class="py-line"><tt class="py-docstring">    # 1'st and 2'nd derivative of exp(x), at x == 1</tt> </tt>
<a name="L78"></a><tt class="py-lineno"> 78</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; import numpy as np</tt> </tt>
<a name="L79"></a><tt class="py-lineno"> 79</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; import numdifftools.nd_algopy as nda</tt> </tt>
<a name="L80"></a><tt class="py-lineno"> 80</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fd = nda.Derivative(np.exp)              # 1'st derivative</tt> </tt>
<a name="L81"></a><tt class="py-lineno"> 81</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fd(1)</tt> </tt>
<a name="L82"></a><tt class="py-lineno"> 82</tt>  <tt class="py-line"><tt class="py-docstring">    array(2.718281828459045)</tt> </tt>
<a name="L83"></a><tt class="py-lineno"> 83</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L84"></a><tt class="py-lineno"> 84</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L85"></a><tt class="py-lineno"> 85</tt>  <tt class="py-line"><tt class="py-docstring">    # 1'st derivative of x.^3+x.^4, at x = [0,1]</tt> </tt>
<a name="L86"></a><tt class="py-lineno"> 86</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fun = lambda x: x**3 + x**4</tt> </tt>
<a name="L87"></a><tt class="py-lineno"> 87</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fd3 = nda.Derivative(fun)</tt> </tt>
<a name="L88"></a><tt class="py-lineno"> 88</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fd3([0,1])          #  True derivatives: [0,7]</tt> </tt>
<a name="L89"></a><tt class="py-lineno"> 89</tt>  <tt class="py-line"><tt class="py-docstring">    array([ 0.,  7.])</tt> </tt>
<a name="L90"></a><tt class="py-lineno"> 90</tt>  <tt class="py-line"><tt class="py-docstring"> </tt> </tt>
<a name="L91"></a><tt class="py-lineno"> 91</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L92"></a><tt class="py-lineno"> 92</tt>  <tt class="py-line"><tt class="py-docstring">    See also</tt> </tt>
<a name="L93"></a><tt class="py-lineno"> 93</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L94"></a><tt class="py-lineno"> 94</tt>  <tt class="py-line"><tt class="py-docstring">    Gradient,</tt> </tt>
<a name="L95"></a><tt class="py-lineno"> 95</tt>  <tt class="py-line"><tt class="py-docstring">    Hessdiag,</tt> </tt>
<a name="L96"></a><tt class="py-lineno"> 96</tt>  <tt class="py-line"><tt class="py-docstring">    Hessian,</tt> </tt>
<a name="L97"></a><tt class="py-lineno"> 97</tt>  <tt class="py-line"><tt class="py-docstring">    Jacobian</tt> </tt>
<a name="L98"></a><tt class="py-lineno"> 98</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="Derivative.derivative"></a><div id="Derivative.derivative-def"><a name="L99"></a><tt class="py-lineno"> 99</tt> <a class="py-toggle" href="#" id="Derivative.derivative-toggle" onclick="return toggle('Derivative.derivative');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Derivative-class.html#derivative">derivative</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Derivative.derivative-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Derivative.derivative-expanded"><a name="L100"></a><tt class="py-lineno">100</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-20" class="py-name" targets="Method numdifftools.core._Derivative._derivative()=numdifftools.core._Derivative-class.html#_derivative,Method numdifftools.nd_algopy._Common._derivative()=numdifftools.nd_algopy._Common-class.html#_derivative,Method numdifftools.nd_scientific._Common._derivative()=numdifftools.nd_scientific._Common-class.html#_derivative"><a title="numdifftools.core._Derivative._derivative
numdifftools.nd_algopy._Common._derivative
numdifftools.nd_scientific._Common._derivative" class="py-name" href="#" onclick="return doclink('link-20', '_derivative', 'link-20');">_derivative</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div><a name="Derivative.__call__"></a><div id="Derivative.__call__-def"><a name="L101"></a><tt class="py-lineno">101</tt> <a class="py-toggle" href="#" id="Derivative.__call__-toggle" onclick="return toggle('Derivative.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Derivative-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Derivative.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Derivative.__call__-expanded"><a name="L102"></a><tt class="py-lineno">102</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-21" class="py-name"><a title="numdifftools.core._Derivative._derivative
numdifftools.nd_algopy._Common._derivative
numdifftools.nd_scientific._Common._derivative" class="py-name" href="#" onclick="return doclink('link-21', '_derivative', 'link-20');">_derivative</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L103"></a><tt class="py-lineno">103</tt>  <tt class="py-line"> </tt>
<a name="Jacobian"></a><div id="Jacobian-def"><a name="L104"></a><tt class="py-lineno">104</tt> <a class="py-toggle" href="#" id="Jacobian-toggle" onclick="return toggle('Jacobian');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Jacobian-class.html">Jacobian</a><tt class="py-op">(</tt><tt class="py-base-class">_Common</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Jacobian-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Jacobian-expanded"><a name="L105"></a><tt class="py-lineno">105</tt>  <tt class="py-line">    <tt class="py-docstring">'''Estimate Jacobian matrix</tt> </tt>
<a name="L106"></a><tt class="py-lineno">106</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L107"></a><tt class="py-lineno">107</tt>  <tt class="py-line"><tt class="py-docstring">    The Jacobian matrix is the matrix of all first-order partial derivatives</tt> </tt>
<a name="L108"></a><tt class="py-lineno">108</tt>  <tt class="py-line"><tt class="py-docstring">    of a vector-valued function.</tt> </tt>
<a name="L109"></a><tt class="py-lineno">109</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L110"></a><tt class="py-lineno">110</tt>  <tt class="py-line"><tt class="py-docstring">    Assumptions</tt> </tt>
<a name="L111"></a><tt class="py-lineno">111</tt>  <tt class="py-line"><tt class="py-docstring">    -----------</tt> </tt>
<a name="L112"></a><tt class="py-lineno">112</tt>  <tt class="py-line"><tt class="py-docstring">    fun : (vector valued)</tt> </tt>
<a name="L113"></a><tt class="py-lineno">113</tt>  <tt class="py-line"><tt class="py-docstring">        analytical function to differentiate.</tt> </tt>
<a name="L114"></a><tt class="py-lineno">114</tt>  <tt class="py-line"><tt class="py-docstring">        fun must be a function of the vector or array x0.</tt> </tt>
<a name="L115"></a><tt class="py-lineno">115</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L116"></a><tt class="py-lineno">116</tt>  <tt class="py-line"><tt class="py-docstring">    x0 : vector location at which to differentiate fun</tt> </tt>
<a name="L117"></a><tt class="py-lineno">117</tt>  <tt class="py-line"><tt class="py-docstring">        If x0 is an N x M array, then fun is assumed to be</tt> </tt>
<a name="L118"></a><tt class="py-lineno">118</tt>  <tt class="py-line"><tt class="py-docstring">        a function of N*M variables.</tt> </tt>
<a name="L119"></a><tt class="py-lineno">119</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L120"></a><tt class="py-lineno">120</tt>  <tt class="py-line"><tt class="py-docstring">    Examples</tt> </tt>
<a name="L121"></a><tt class="py-lineno">121</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L122"></a><tt class="py-lineno">122</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; import numdifftools.nd_algopy as nda</tt> </tt>
<a name="L123"></a><tt class="py-lineno">123</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L124"></a><tt class="py-lineno">124</tt>  <tt class="py-line"><tt class="py-docstring">    #(nonlinear least squares)</tt> </tt>
<a name="L125"></a><tt class="py-lineno">125</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; xdata = np.reshape(np.arange(0,1,0.1),(-1,1))</tt> </tt>
<a name="L126"></a><tt class="py-lineno">126</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; ydata = 1+2*np.exp(0.75*xdata)</tt> </tt>
<a name="L127"></a><tt class="py-lineno">127</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2</tt> </tt>
<a name="L128"></a><tt class="py-lineno">128</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L129"></a><tt class="py-lineno">129</tt>  <tt class="py-line"><tt class="py-docstring">    Jfun = nda.Jacobian(fun) # Todo: This does not work</tt> </tt>
<a name="L130"></a><tt class="py-lineno">130</tt>  <tt class="py-line"><tt class="py-docstring">    Jfun([1,2,0.75]) # should be numerically zero</tt> </tt>
<a name="L131"></a><tt class="py-lineno">131</tt>  <tt class="py-line"><tt class="py-docstring">    array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],</tt> </tt>
<a name="L132"></a><tt class="py-lineno">132</tt>  <tt class="py-line"><tt class="py-docstring">           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],</tt> </tt>
<a name="L133"></a><tt class="py-lineno">133</tt>  <tt class="py-line"><tt class="py-docstring">           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])</tt> </tt>
<a name="L134"></a><tt class="py-lineno">134</tt>  <tt class="py-line"><tt class="py-docstring"> </tt> </tt>
<a name="L135"></a><tt class="py-lineno">135</tt>  <tt class="py-line"><tt class="py-docstring">    Jfun2 = Jacobian(fun, method='reverse')</tt> </tt>
<a name="L136"></a><tt class="py-lineno">136</tt>  <tt class="py-line"><tt class="py-docstring">    Jfun2([1,2,0.75]) # should be numerically zero</tt> </tt>
<a name="L137"></a><tt class="py-lineno">137</tt>  <tt class="py-line"><tt class="py-docstring">    array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],</tt> </tt>
<a name="L138"></a><tt class="py-lineno">138</tt>  <tt class="py-line"><tt class="py-docstring">           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],</tt> </tt>
<a name="L139"></a><tt class="py-lineno">139</tt>  <tt class="py-line"><tt class="py-docstring">           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])</tt> </tt>
<a name="L140"></a><tt class="py-lineno">140</tt>  <tt class="py-line"><tt class="py-docstring">           </tt> </tt>
<a name="L141"></a><tt class="py-lineno">141</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fun2 = lambda x : x[0]*x[1]*x[2] + np.exp(x[0])*x[1]</tt> </tt>
<a name="L142"></a><tt class="py-lineno">142</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; Jfun3 = nda.Jacobian(fun2)</tt> </tt>
<a name="L143"></a><tt class="py-lineno">143</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; Jfun3([3.,5.,7.])</tt> </tt>
<a name="L144"></a><tt class="py-lineno">144</tt>  <tt class="py-line"><tt class="py-docstring">    array([ 135.42768462,   41.08553692,   15.        ])</tt> </tt>
<a name="L145"></a><tt class="py-lineno">145</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L146"></a><tt class="py-lineno">146</tt>  <tt class="py-line"><tt class="py-docstring">    Jfun4 = nda.Jacobian(fun2, method='reverse')</tt> </tt>
<a name="L147"></a><tt class="py-lineno">147</tt>  <tt class="py-line"><tt class="py-docstring">    Jfun4([3,5,7])</tt> </tt>
<a name="L148"></a><tt class="py-lineno">148</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L149"></a><tt class="py-lineno">149</tt>  <tt class="py-line"><tt class="py-docstring">    See also</tt> </tt>
<a name="L150"></a><tt class="py-lineno">150</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L151"></a><tt class="py-lineno">151</tt>  <tt class="py-line"><tt class="py-docstring">    Gradient,</tt> </tt>
<a name="L152"></a><tt class="py-lineno">152</tt>  <tt class="py-line"><tt class="py-docstring">    Derivative,</tt> </tt>
<a name="L153"></a><tt class="py-lineno">153</tt>  <tt class="py-line"><tt class="py-docstring">    Hessdiag,</tt> </tt>
<a name="L154"></a><tt class="py-lineno">154</tt>  <tt class="py-line"><tt class="py-docstring">    Hessian</tt> </tt>
<a name="L155"></a><tt class="py-lineno">155</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="Jacobian.__call__"></a><div id="Jacobian.__call__-def"><a name="L156"></a><tt class="py-lineno">156</tt> <a class="py-toggle" href="#" id="Jacobian.__call__-toggle" onclick="return toggle('Jacobian.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Jacobian-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Jacobian.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Jacobian.__call__-expanded"><a name="L157"></a><tt class="py-lineno">157</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-22" class="py-name"><a title="numdifftools.core.Jacobian.jacobian
numdifftools.nd_algopy.Jacobian.jacobian
numdifftools.nd_scientific.Jacobian.jacobian" class="py-name" href="#" onclick="return doclink('link-22', 'jacobian', 'link-15');">jacobian</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div><a name="L158"></a><tt class="py-lineno">158</tt>  <tt class="py-line"> </tt>
<a name="Jacobian.jacobian"></a><div id="Jacobian.jacobian-def"><a name="L159"></a><tt class="py-lineno">159</tt> <a class="py-toggle" href="#" id="Jacobian.jacobian-toggle" onclick="return toggle('Jacobian.jacobian');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Jacobian-class.html#jacobian">jacobian</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Jacobian.jacobian-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Jacobian.jacobian-expanded"><a name="L160"></a><tt class="py-lineno">160</tt>  <tt class="py-line">        <tt class="py-docstring">'''</tt> </tt>
<a name="L161"></a><tt class="py-lineno">161</tt>  <tt class="py-line"><tt class="py-docstring">        Return Jacobian matrix of a vector valued function of n variables</tt> </tt>
<a name="L162"></a><tt class="py-lineno">162</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L163"></a><tt class="py-lineno">163</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L164"></a><tt class="py-lineno">164</tt>  <tt class="py-line"><tt class="py-docstring">        Parameter</tt> </tt>
<a name="L165"></a><tt class="py-lineno">165</tt>  <tt class="py-line"><tt class="py-docstring">        ---------</tt> </tt>
<a name="L166"></a><tt class="py-lineno">166</tt>  <tt class="py-line"><tt class="py-docstring">        x0 : vector</tt> </tt>
<a name="L167"></a><tt class="py-lineno">167</tt>  <tt class="py-line"><tt class="py-docstring">            location at which to differentiate fun.</tt> </tt>
<a name="L168"></a><tt class="py-lineno">168</tt>  <tt class="py-line"><tt class="py-docstring">            If x0 is an nxm array, then fun is assumed to be</tt> </tt>
<a name="L169"></a><tt class="py-lineno">169</tt>  <tt class="py-line"><tt class="py-docstring">            a function of n*m variables.</tt> </tt>
<a name="L170"></a><tt class="py-lineno">170</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L171"></a><tt class="py-lineno">171</tt>  <tt class="py-line"><tt class="py-docstring">        Member variable used</tt> </tt>
<a name="L172"></a><tt class="py-lineno">172</tt>  <tt class="py-line"><tt class="py-docstring">        --------------------</tt> </tt>
<a name="L173"></a><tt class="py-lineno">173</tt>  <tt class="py-line"><tt class="py-docstring">        fun : (vector valued) analytical function to differentiate.</tt> </tt>
<a name="L174"></a><tt class="py-lineno">174</tt>  <tt class="py-line"><tt class="py-docstring">                fun must be a function of the vector or array x0.</tt> </tt>
<a name="L175"></a><tt class="py-lineno">175</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L176"></a><tt class="py-lineno">176</tt>  <tt class="py-line"><tt class="py-docstring">        Returns</tt> </tt>
<a name="L177"></a><tt class="py-lineno">177</tt>  <tt class="py-line"><tt class="py-docstring">        -------</tt> </tt>
<a name="L178"></a><tt class="py-lineno">178</tt>  <tt class="py-line"><tt class="py-docstring">        jac : array-like</tt> </tt>
<a name="L179"></a><tt class="py-lineno">179</tt>  <tt class="py-line"><tt class="py-docstring">           first partial derivatives of fun. Assuming that x0</tt> </tt>
<a name="L180"></a><tt class="py-lineno">180</tt>  <tt class="py-line"><tt class="py-docstring">           is a vector of length p and fun returns a vector</tt> </tt>
<a name="L181"></a><tt class="py-lineno">181</tt>  <tt class="py-line"><tt class="py-docstring">           of length n, then jac will be an array of size (n,p)</tt> </tt>
<a name="L182"></a><tt class="py-lineno">182</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L183"></a><tt class="py-lineno">183</tt>  <tt class="py-line"><tt class="py-docstring">        err - vector</tt> </tt>
<a name="L184"></a><tt class="py-lineno">184</tt>  <tt class="py-line"><tt class="py-docstring">            of error estimates corresponding to each partial</tt> </tt>
<a name="L185"></a><tt class="py-lineno">185</tt>  <tt class="py-line"><tt class="py-docstring">            derivative in jac.</tt> </tt>
<a name="L186"></a><tt class="py-lineno">186</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L187"></a><tt class="py-lineno">187</tt>  <tt class="py-line"><tt class="py-docstring">        See also</tt> </tt>
<a name="L188"></a><tt class="py-lineno">188</tt>  <tt class="py-line"><tt class="py-docstring">        --------</tt> </tt>
<a name="L189"></a><tt class="py-lineno">189</tt>  <tt class="py-line"><tt class="py-docstring">        Derivative,</tt> </tt>
<a name="L190"></a><tt class="py-lineno">190</tt>  <tt class="py-line"><tt class="py-docstring">        Gradient,</tt> </tt>
<a name="L191"></a><tt class="py-lineno">191</tt>  <tt class="py-line"><tt class="py-docstring">        Hessian,</tt> </tt>
<a name="L192"></a><tt class="py-lineno">192</tt>  <tt class="py-line"><tt class="py-docstring">        Hessdiag</tt> </tt>
<a name="L193"></a><tt class="py-lineno">193</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L194"></a><tt class="py-lineno">194</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-23" class="py-name"><a title="numdifftools.nd_scientific._Common._jacobian" class="py-name" href="#" onclick="return doclink('link-23', '_jacobian', 'link-5');">_jacobian</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt>   </tt>
</div></div><a name="Gradient"></a><div id="Gradient-def"><a name="L195"></a><tt class="py-lineno">195</tt> <a class="py-toggle" href="#" id="Gradient-toggle" onclick="return toggle('Gradient');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Gradient-class.html">Gradient</a><tt class="py-op">(</tt><tt class="py-base-class">_Common</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Gradient-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Gradient-expanded"><a name="L196"></a><tt class="py-lineno">196</tt>  <tt class="py-line">    <tt class="py-docstring">'''Estimate gradient of fun at x0</tt> </tt>
<a name="L197"></a><tt class="py-lineno">197</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L198"></a><tt class="py-lineno">198</tt>  <tt class="py-line"><tt class="py-docstring">    Assumptions</tt> </tt>
<a name="L199"></a><tt class="py-lineno">199</tt>  <tt class="py-line"><tt class="py-docstring">    -----------</tt> </tt>
<a name="L200"></a><tt class="py-lineno">200</tt>  <tt class="py-line"><tt class="py-docstring">      fun - SCALAR analytical function to differentiate.</tt> </tt>
<a name="L201"></a><tt class="py-lineno">201</tt>  <tt class="py-line"><tt class="py-docstring">            fun must be a function of the vector or array x0,</tt> </tt>
<a name="L202"></a><tt class="py-lineno">202</tt>  <tt class="py-line"><tt class="py-docstring">            but it needs not to be vectorized.</tt> </tt>
<a name="L203"></a><tt class="py-lineno">203</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L204"></a><tt class="py-lineno">204</tt>  <tt class="py-line"><tt class="py-docstring">      x0  - vector location at which to differentiate fun</tt> </tt>
<a name="L205"></a><tt class="py-lineno">205</tt>  <tt class="py-line"><tt class="py-docstring">            If x0 is an N x M array, then fun is assumed to be</tt> </tt>
<a name="L206"></a><tt class="py-lineno">206</tt>  <tt class="py-line"><tt class="py-docstring">            a function of N*M variables.</tt> </tt>
<a name="L207"></a><tt class="py-lineno">207</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L208"></a><tt class="py-lineno">208</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L209"></a><tt class="py-lineno">209</tt>  <tt class="py-line"><tt class="py-docstring">    Examples</tt> </tt>
<a name="L210"></a><tt class="py-lineno">210</tt>  <tt class="py-line"><tt class="py-docstring">    -------- </tt> </tt>
<a name="L211"></a><tt class="py-lineno">211</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; import numdifftools.nd_algopy as nda</tt> </tt>
<a name="L212"></a><tt class="py-lineno">212</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fun = lambda x: np.sum(x**2)</tt> </tt>
<a name="L213"></a><tt class="py-lineno">213</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; dfun = nda.Gradient(fun)</tt> </tt>
<a name="L214"></a><tt class="py-lineno">214</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; dfun([1,2,3])</tt> </tt>
<a name="L215"></a><tt class="py-lineno">215</tt>  <tt class="py-line"><tt class="py-docstring">    array([ 2.,  4.,  6.])</tt> </tt>
<a name="L216"></a><tt class="py-lineno">216</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L217"></a><tt class="py-lineno">217</tt>  <tt class="py-line"><tt class="py-docstring">    #At [x,y] = [1,1], compute the numerical gradient</tt> </tt>
<a name="L218"></a><tt class="py-lineno">218</tt>  <tt class="py-line"><tt class="py-docstring">    #of the function sin(x-y) + y*exp(x)</tt> </tt>
<a name="L219"></a><tt class="py-lineno">219</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L220"></a><tt class="py-lineno">220</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; sin = np.sin; exp = np.exp</tt> </tt>
<a name="L221"></a><tt class="py-lineno">221</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; z = lambda xy: sin(xy[0]-xy[1]) + xy[1]*exp(xy[0])</tt> </tt>
<a name="L222"></a><tt class="py-lineno">222</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; dz = nda.Gradient(z)</tt> </tt>
<a name="L223"></a><tt class="py-lineno">223</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; grad2 = dz([1, 1])</tt> </tt>
<a name="L224"></a><tt class="py-lineno">224</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; grad2</tt> </tt>
<a name="L225"></a><tt class="py-lineno">225</tt>  <tt class="py-line"><tt class="py-docstring">    array([ 3.71828183,  1.71828183])</tt> </tt>
<a name="L226"></a><tt class="py-lineno">226</tt>  <tt class="py-line"><tt class="py-docstring">     </tt> </tt>
<a name="L227"></a><tt class="py-lineno">227</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L228"></a><tt class="py-lineno">228</tt>  <tt class="py-line"><tt class="py-docstring">    #At the global minimizer (1,1) of the Rosenbrock function,</tt> </tt>
<a name="L229"></a><tt class="py-lineno">229</tt>  <tt class="py-line"><tt class="py-docstring">    #compute the gradient. It should be essentially zero.</tt> </tt>
<a name="L230"></a><tt class="py-lineno">230</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L231"></a><tt class="py-lineno">231</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; rosen = lambda x : (1-x[0])**2 + 105.*(x[1]-x[0]**2)**2</tt> </tt>
<a name="L232"></a><tt class="py-lineno">232</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; rd = nda.Gradient(rosen)</tt> </tt>
<a name="L233"></a><tt class="py-lineno">233</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; grad3 = rd([1,1])</tt> </tt>
<a name="L234"></a><tt class="py-lineno">234</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; grad3==np.array([ 0.,  0.])</tt> </tt>
<a name="L235"></a><tt class="py-lineno">235</tt>  <tt class="py-line"><tt class="py-docstring">    array([ True,  True], dtype=bool)</tt> </tt>
<a name="L236"></a><tt class="py-lineno">236</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L237"></a><tt class="py-lineno">237</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L238"></a><tt class="py-lineno">238</tt>  <tt class="py-line"><tt class="py-docstring">    See also</tt> </tt>
<a name="L239"></a><tt class="py-lineno">239</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L240"></a><tt class="py-lineno">240</tt>  <tt class="py-line"><tt class="py-docstring">    Derivative, Hessdiag, Hessian, Jacobian</tt> </tt>
<a name="L241"></a><tt class="py-lineno">241</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="L242"></a><tt class="py-lineno">242</tt>  <tt class="py-line"> </tt>
<a name="Gradient.gradient"></a><div id="Gradient.gradient-def"><a name="L243"></a><tt class="py-lineno">243</tt> <a class="py-toggle" href="#" id="Gradient.gradient-toggle" onclick="return toggle('Gradient.gradient');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Gradient-class.html#gradient">gradient</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Gradient.gradient-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Gradient.gradient-expanded"><a name="L244"></a><tt class="py-lineno">244</tt>  <tt class="py-line">        <tt class="py-docstring">''' Gradient vector of an analytical function of n variables</tt> </tt>
<a name="L245"></a><tt class="py-lineno">245</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L246"></a><tt class="py-lineno">246</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-24" class="py-name"><a title="numdifftools.nd_scientific._Common._gradient" class="py-name" href="#" onclick="return doclink('link-24', '_gradient', 'link-1');">_gradient</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div><a name="L247"></a><tt class="py-lineno">247</tt>  <tt class="py-line">         </tt>
<a name="Gradient.__call__"></a><div id="Gradient.__call__-def"><a name="L248"></a><tt class="py-lineno">248</tt> <a class="py-toggle" href="#" id="Gradient.__call__-toggle" onclick="return toggle('Gradient.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Gradient-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt>  </tt>
</div><a name="L249"></a><tt class="py-lineno">249</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-25" class="py-name"><a title="numdifftools.nd_scientific._Common._gradient" class="py-name" href="#" onclick="return doclink('link-25', '_gradient', 'link-1');">_gradient</a></tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
</div></div><a name="L250"></a><tt class="py-lineno">250</tt>  <tt class="py-line">     </tt>
<a name="Hessian"></a><div id="Hessian-def"><a name="L251"></a><tt class="py-lineno">251</tt> <a class="py-toggle" href="#" id="Hessian-toggle" onclick="return toggle('Hessian');">-</a><tt class="py-line"><tt class="py-keyword">class</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Hessian-class.html">Hessian</a><tt class="py-op">(</tt><tt class="py-base-class">_Common</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessian-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="Hessian-expanded"><a name="L252"></a><tt class="py-lineno">252</tt>  <tt class="py-line">    <tt class="py-docstring">''' Estimate Hessian matrix </tt> </tt>
<a name="L253"></a><tt class="py-lineno">253</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L254"></a><tt class="py-lineno">254</tt>  <tt class="py-line"><tt class="py-docstring">    HESSIAN estimate the matrix of 2nd order partial derivatives of a real</tt> </tt>
<a name="L255"></a><tt class="py-lineno">255</tt>  <tt class="py-line"><tt class="py-docstring">    valued function FUN evaluated at X0.  </tt> </tt>
<a name="L256"></a><tt class="py-lineno">256</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L257"></a><tt class="py-lineno">257</tt>  <tt class="py-line"><tt class="py-docstring">    Assumptions</tt> </tt>
<a name="L258"></a><tt class="py-lineno">258</tt>  <tt class="py-line"><tt class="py-docstring">    -----------</tt> </tt>
<a name="L259"></a><tt class="py-lineno">259</tt>  <tt class="py-line"><tt class="py-docstring">    fun : SCALAR analytical function</tt> </tt>
<a name="L260"></a><tt class="py-lineno">260</tt>  <tt class="py-line"><tt class="py-docstring">        to differentiate. fun must be a function of the vector or array x0,</tt> </tt>
<a name="L261"></a><tt class="py-lineno">261</tt>  <tt class="py-line"><tt class="py-docstring">        but it needs not to be vectorized.</tt> </tt>
<a name="L262"></a><tt class="py-lineno">262</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L263"></a><tt class="py-lineno">263</tt>  <tt class="py-line"><tt class="py-docstring">    x0 : vector location</tt> </tt>
<a name="L264"></a><tt class="py-lineno">264</tt>  <tt class="py-line"><tt class="py-docstring">        at which to differentiate fun</tt> </tt>
<a name="L265"></a><tt class="py-lineno">265</tt>  <tt class="py-line"><tt class="py-docstring">        If x0 is an N x M array, then fun is assumed to be a function</tt> </tt>
<a name="L266"></a><tt class="py-lineno">266</tt>  <tt class="py-line"><tt class="py-docstring">        of N*M variables.</tt> </tt>
<a name="L267"></a><tt class="py-lineno">267</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L268"></a><tt class="py-lineno">268</tt>  <tt class="py-line"><tt class="py-docstring">    Examples</tt> </tt>
<a name="L269"></a><tt class="py-lineno">269</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L270"></a><tt class="py-lineno">270</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; import numdifftools.nd_algopy as nda</tt> </tt>
<a name="L271"></a><tt class="py-lineno">271</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L272"></a><tt class="py-lineno">272</tt>  <tt class="py-line"><tt class="py-docstring">    #Rosenbrock function, minimized at [1,1]</tt> </tt>
<a name="L273"></a><tt class="py-lineno">273</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; rosen = lambda x : (1.-x[0])**2 + 105*(x[1]-x[0]**2)**2</tt> </tt>
<a name="L274"></a><tt class="py-lineno">274</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; Hfun = nda.Hessian(rosen)</tt> </tt>
<a name="L275"></a><tt class="py-lineno">275</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; h = Hfun([1, 1]) #  h =[ 842 -420; -420, 210];</tt> </tt>
<a name="L276"></a><tt class="py-lineno">276</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; h</tt> </tt>
<a name="L277"></a><tt class="py-lineno">277</tt>  <tt class="py-line"><tt class="py-docstring">    array([[ 842., -420.],</tt> </tt>
<a name="L278"></a><tt class="py-lineno">278</tt>  <tt class="py-line"><tt class="py-docstring">           [-420.,  210.]])</tt> </tt>
<a name="L279"></a><tt class="py-lineno">279</tt>  <tt class="py-line"><tt class="py-docstring">     </tt> </tt>
<a name="L280"></a><tt class="py-lineno">280</tt>  <tt class="py-line"><tt class="py-docstring">    #cos(x-y), at (0,0)</tt> </tt>
<a name="L281"></a><tt class="py-lineno">281</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; cos = np.cos</tt> </tt>
<a name="L282"></a><tt class="py-lineno">282</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; fun = lambda xy : cos(xy[0]-xy[1])</tt> </tt>
<a name="L283"></a><tt class="py-lineno">283</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; Hfun2 = nda.Hessian(fun)</tt> </tt>
<a name="L284"></a><tt class="py-lineno">284</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; h2 = Hfun2([0, 0]) # h2 = [-1 1; 1 -1] </tt> </tt>
<a name="L285"></a><tt class="py-lineno">285</tt>  <tt class="py-line"><tt class="py-docstring">    &gt;&gt;&gt; h2</tt> </tt>
<a name="L286"></a><tt class="py-lineno">286</tt>  <tt class="py-line"><tt class="py-docstring">    array([[-1.,  1.],</tt> </tt>
<a name="L287"></a><tt class="py-lineno">287</tt>  <tt class="py-line"><tt class="py-docstring">           [ 1., -1.]])</tt> </tt>
<a name="L288"></a><tt class="py-lineno">288</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L289"></a><tt class="py-lineno">289</tt>  <tt class="py-line"><tt class="py-docstring">    Hfun3 = Hessian(fun, method='reverse') # TODO: Hfun3 fails in this case</tt> </tt>
<a name="L290"></a><tt class="py-lineno">290</tt>  <tt class="py-line"><tt class="py-docstring">    h3 = Hfun3([0, 0]) # h2 = [-1, 1; 1, -1];</tt> </tt>
<a name="L291"></a><tt class="py-lineno">291</tt>  <tt class="py-line"><tt class="py-docstring">    h3</tt> </tt>
<a name="L292"></a><tt class="py-lineno">292</tt>  <tt class="py-line"><tt class="py-docstring">    array([[[-1.,  1.],</tt> </tt>
<a name="L293"></a><tt class="py-lineno">293</tt>  <tt class="py-line"><tt class="py-docstring">            [ 1., -1.]]])</tt> </tt>
<a name="L294"></a><tt class="py-lineno">294</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L295"></a><tt class="py-lineno">295</tt>  <tt class="py-line"><tt class="py-docstring">    See also</tt> </tt>
<a name="L296"></a><tt class="py-lineno">296</tt>  <tt class="py-line"><tt class="py-docstring">    --------</tt> </tt>
<a name="L297"></a><tt class="py-lineno">297</tt>  <tt class="py-line"><tt class="py-docstring">    Gradient,</tt> </tt>
<a name="L298"></a><tt class="py-lineno">298</tt>  <tt class="py-line"><tt class="py-docstring">    Derivative,</tt> </tt>
<a name="L299"></a><tt class="py-lineno">299</tt>  <tt class="py-line"><tt class="py-docstring">    Hessdiag,</tt> </tt>
<a name="L300"></a><tt class="py-lineno">300</tt>  <tt class="py-line"><tt class="py-docstring">    Jacobian</tt> </tt>
<a name="L301"></a><tt class="py-lineno">301</tt>  <tt class="py-line"><tt class="py-docstring">    '''</tt> </tt>
<a name="L302"></a><tt class="py-lineno">302</tt>  <tt class="py-line">     </tt>
<a name="Hessian.hessian"></a><div id="Hessian.hessian-def"><a name="L303"></a><tt class="py-lineno">303</tt> <a class="py-toggle" href="#" id="Hessian.hessian-toggle" onclick="return toggle('Hessian.hessian');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Hessian-class.html#hessian">hessian</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessian.hessian-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Hessian.hessian-expanded"><a name="L304"></a><tt class="py-lineno">304</tt>  <tt class="py-line">        <tt class="py-docstring">'''Hessian matrix i.e., array of 2nd order partial derivatives</tt> </tt>
<a name="L305"></a><tt class="py-lineno">305</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L306"></a><tt class="py-lineno">306</tt>  <tt class="py-line"><tt class="py-docstring">        See also </tt> </tt>
<a name="L307"></a><tt class="py-lineno">307</tt>  <tt class="py-line"><tt class="py-docstring">        derivative, gradient, hessdiag, jacobian</tt> </tt>
<a name="L308"></a><tt class="py-lineno">308</tt>  <tt class="py-line"><tt class="py-docstring">        '''</tt> </tt>
<a name="L309"></a><tt class="py-lineno">309</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-26" class="py-name"><a title="numdifftools.nd_scientific._Common._hessian" class="py-name" href="#" onclick="return doclink('link-26', '_hessian', 'link-3');">_hessian</a></tt><tt class="py-op">(</tt><tt class="py-name">x0</tt><tt class="py-op">)</tt> </tt>
</div><a name="L310"></a><tt class="py-lineno">310</tt>  <tt class="py-line">      </tt>
<a name="Hessian.__call__"></a><div id="Hessian.__call__-def"><a name="L311"></a><tt class="py-lineno">311</tt> <a class="py-toggle" href="#" id="Hessian.__call__-toggle" onclick="return toggle('Hessian.__call__');">-</a><tt class="py-line">    <tt class="py-keyword">def</tt> <a class="py-def-name" href="numdifftools.nd_algopy.Hessian-class.html#__call__">__call__</a><tt class="py-op">(</tt><tt class="py-param">self</tt><tt class="py-op">,</tt> <tt class="py-param">x</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="Hessian.__call__-collapsed" style="display:none;" pad="+++" indent="++++++++"></div><div id="Hessian.__call__-expanded"><a name="L312"></a><tt class="py-lineno">312</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">self</tt><tt class="py-op">.</tt><tt id="link-27" class="py-name"><a title="numdifftools.nd_scientific._Common._hessian" class="py-name" href="#" onclick="return doclink('link-27', '_hessian', 'link-3');">_hessian</a></tt><tt class="py-op">(</tt><tt class="py-name">x</tt><tt class="py-op">)</tt>  </tt>
</div></div><a name="L313"></a><tt class="py-lineno">313</tt>  <tt class="py-line">     </tt>
<a name="L314"></a><tt class="py-lineno">314</tt>  <tt class="py-line">  </tt>
<a name="L315"></a><tt class="py-lineno">315</tt>  <tt class="py-line"><tt class="py-keyword">if</tt> <tt class="py-name">__name__</tt> <tt class="py-op">==</tt> <tt class="py-string">'__main__'</tt><tt class="py-op">:</tt> </tt>
<a name="L316"></a><tt class="py-lineno">316</tt>  <tt class="py-line">    <tt class="py-keyword">import</tt> <tt class="py-name">doctest</tt> </tt>
<a name="L317"></a><tt class="py-lineno">317</tt>  <tt class="py-line">    <tt class="py-name">doctest</tt><tt class="py-op">.</tt><tt class="py-name">testmod</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L318"></a><tt class="py-lineno">318</tt>  <tt class="py-line"> </tt><script type="text/javascript">
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